Describe motion in terms of frame of reference Express scalar and vector quantities Understand the relationship between scalar and vector quantities

Motion One-dimensional motion is the simplest form of motion – A change in position – Motion that takes place in one direction -X or Y direction but not simultaneously

Motion takes place over time and depends upon the frame of reference Frame of reference – a coordinate system for specifying the precise location of objects in space; a point that is used to compare another objects motion

Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it; it has nothing to do with spacial direction Magnitude – A numerical value with units. Scalar Example Magnitude Speed20 m/s Distance10 m Age15 years Heat1000 calories

Vector A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION. VectorMagnitude & Direction Velocity20 m/s, N Acceleration10 m/s/s, E Force5 N, West Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

More about Vectors A vector is represented on paper by an arrow 1. the length represents magnitude 2. the arrow faces the direction of motion

Vectors can be added graphically Resultant – answer found by adding vectors

Vectors can be added graphically The goal is to draw a mini version of the vectors to give you an accurate picture of the magnitude and direction. To do so, you must: 1.Pick a scale to represent the vectors. Make it simple yet appropriate. 2.Draw the tip of the vector as an arrow pointing in the appropriate direction. 3.Use a ruler & protractor to draw arrows for accuracy. The angle is always measured from the horizontal or vertical where the motion started.

Vectors can be moved parallel to themselves in a diagram Vectors can be added in any order To subtract a vector, add its opposite Vectors can be added graphically

Determining resultant magnitude If the movement is in straight lines that form a right triangle, Use the Pythagorean theorem to find the magnitude of the resultant

Pythagorean Theorem for right triangles d 2 = x 2 + y 2 (Length of hypotenuse) 2 = (length of one leg) 2 + (length of the other leg) 2 Determining resultant magnitude

To completely describe the resultant you also need to find the direction also When the resultant forms a right triangle, use the tangent function to find the angle (θ) of the resultant Determining resultant direction

DETERMINING DIRECTION B A C D N of E N of W S of W S of E

The angle (θ) of the resultant is the direction of the resultant Determining resultant direction

To find just the angle, use the inverse of the tangent function

Remember when you solve for the displacement you are looking for the magnitude (d) and the direction (Θ with descriptor)

Kangaroos can easily jump as far as 8.0m. If a kangaroo makes five such jumps westward, how many jumps must it take northward to have a northwest displacement with a magnitude of 68m? What is the angle of the resultant displacement with respect to the north?

The emperor penguin is the best diver among birds: the record dive is 483m. Suppose an emperor penguin dives vertically to a depth of 483m and then swims horizontally a distance of 225m to the right. What angle would the vector of the resultant displacement make with the water’s surface? What is the magnitude of the penguin’s resultant displacement?